Perfectly secure steganography using minimum entropy coupling

Perfectly Secure Steganography Using Minimum Entropy Coupling.
Steganography is the practice of encoding secret information into innocuous
content in such a manner that an adversarial third party would not realize that
there is hidden meaning. While this problem has classically been studied in
security literature, recent advances in generative models have led to a shared
interest among security and machine learning researchers in developing scalable
steganography techniques. In this work, we show that a steganography procedure
is perfectly secure under Cachin (1998)'s information theoretic-model of
steganography if and only if it is induced by a coupling. Furthermore, we show
that, among perfectly secure procedures, a procedure is maximally efficient if
and only if it is induced by a minimum entropy coupling. These insights yield
what are, to the best of our knowledge, the first steganography algorithms to
achieve perfect security guarantees with non-trivial efficiency; additionally,
these algorithms are highly scalable. To provide empirical validation, we
compare a minimum entropy coupling-based approach to three modern baselines –
arithmetic coding, Meteor, and adaptive dynamic grouping – using GPT-2,
WaveRNN, and Image Transformer as communication channels. We find that the
minimum entropy coupling-based approach achieves superior encoding efficiency,
despite its stronger security constraints. In aggregate, these results suggest
that it may be natural to view information-theoretic steganography through the
lens of minimum entropy coupling.

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